Integral equation theory of molecular liquids based on statistical mechanics is quite promising as an essential part of multiscale methodology for chemical and biomolecular nanosystems in solution. Beginning with a molecular interaction potential force field, it uses diagrammatic analysis of the solvation free energy to derive integral equations for correlation functions between molecules in solution in the statistical-mechanical ensemble. The infinite chain of coupled integral equations for many-body correlation functions is reduced to a tractable form for 2- or 3-body correlations by applying the so-called closure relations. Solving these equations produces the solvation structure with accuracy comparable to molecular simulations that have converged but has a critical advantage of readily treating the effects and processes spanning over a large space and slow time scales, by far not feasible for explicit solvent molecular simulations. One of the versions of this formalism, the three-dimensional reference interaction site model (3D-RISM) integral equation complemented with the Kovalenko-Hirata (KH) closure approximation, yields the solvation structure in terms of 3D maps of correlation functions, including density distributions, of solvent interaction sites around a solute (supra)molecule with full consistent account for the effects of chemical functionalities of all species in the solution. The solvation free energy and the subsequent thermodynamics are then obtained at once as a simple integral of the 3D correlation functions by performing thermodynamic integration analytically. Analytical form of the free energy functional permits the self-consistent field coupling of 3D-RISM-KH with quantum chemistry methods in multiscale description of electronic structure in solution, the use of 3D maps of potentials of mean force as scoring functions for molecular recognition and protein-ligand binding in docking protocols for fragment based drug design, and the hybrid MD simulation running quasidynamics of biomolecules steered with 3D-RISM-KH mean solvation forces. The 3D-RISM-KH theory has been validated on both simple and complex associating liquids with different chemical functionalities in a wide range of thermodynamic conditions, at different solid-liquid interfaces, in soft matter, and various environments and confinements. The 3D-RISM-KH theory offers a "mental microscope" capable of providing an insight into structure and molecular mechanisms of formation and functioning of various chemical and biomolecular systems and nanomaterials.